Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models

DOI10.1006/ffta.1999.0266zbMath0972.14025OpenAlexW1991160481MaRDI QIDQ1971065

José I. Farrán, Antonio Campillo

Publication date: 30 October 2001

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.1999.0266

zbMATH Keywords

approximate rootsWeierstrass semigroupalgebraic geometry codeFeng-Rao bound

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Bounds on codes (94B65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Computational aspects of algebraic curves (14Q05) Riemann surfaces; Weierstrass points; gap sequences (14H55)

Related Items (18)

On the evaluation codes given by simple \(\delta \)-sequences ⋮ Suzuki-invariant codes from the Suzuki curve ⋮ Towards a better understanding of the semigroup tree ⋮ Computing the Feng-Rao distances for codes from order domains ⋮ AG codes and AG quantum codes from the GGS curve ⋮ Quantum codes from a new construction of self-orthogonal algebraic geometry codes ⋮ Hermitian-invariant codes from the Hermitian curve ⋮ On Multi-Index Filtrations Associated to Weierstraß Semigroups ⋮ Evaluation codes defined by finite families of plane valuations at infinity ⋮ AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves ⋮ Triples of rational points on the Hermitian curve and their Weierstrass semigroups ⋮ An improvement of the Feng-Rao bound on minimum distance ⋮ Goppa-like bounds for the generalized Feng-Rao distances. ⋮ On the generalized Feng-Rao numbers of numerical semigroups generated by intervals ⋮ Weierstrass semigroup at \(m+1\) rational points in maximal curves which cannot be covered by the Hermitian curve ⋮ Quantum codes from one-point codes on norm-trace curves ⋮ Antonio Campillo ⋮ Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes

Cites Work

• Algebroid curves in positive characteristic
• Die Wertehalbgruppe einer ebenen irreduciblen algebroiden Kurve
• Irreducibility criterion for germs of analytic functions of two complex variables
• Lectures on expansion techniques in algebraic geometry. With notes by Balwant Singh
• Syzygies of affine toric varieties
• Group codes on certain algebraic curves with many rational points
• Decoding algebraic-geometric codes up to the designed minimum distance
• On Planar Curves
• On the decoding of algebraic-geometric codes
• The minimum distance of codes in an array coming from telescopic semigroups
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